Time resolved optical spectroscopy in photodissociation experiments, polarized single crystal absorption spectroscopy, and molecular dynamics simulations are being used to investigate structure function relations in myoglobin and hemoglobin. The technique of high-precision nanosecond spectroscopy in partial photolysis experiments has been developed and has led to several important new findings, including (i) demonstration that the transition state for the quaternary structural change of hemoglobin is much more like the R conformation than the T conformation, a result which explains the linear free energy relation between the quaternary rates and equilibrium constants, (ii) discovery of the protein relaxation subsequent to photodissociation of the myoglobin carbon monoxide complex that may be responsible for a time- dependent barrier to ligand rebinding, (iii) demonstration in hemoglobin that there is no communication between subunits prior to the quaternary conformational change at about 10 microseconds, (iv) and confirmation of theoretical predictions for the dependence of the optical anisotropy on the degree of photolysis with linearly-polarized light pulses. Polarized single crystal absorption measurements show that crystals of hemoglobin in the T quaternary structure bind oxygen noncooperatively with no Bohr effect. These results provide strong evidence for the two-state allosteric model and for Perutz's stereochemical mechanism of the Bohr effect. Studies of the domain structure and kinetics of hemoglobin S gel formati on support the hypothesis that homogeneous nucleation of a single polymer molecule can trigger the formation of an entire domain of polymers, and that variations in the rate of homogeneous nucleation can account for the wide variety of shapes for sickled cells.